def test_racah():
assert racah(3, 3, 3, 3, 3, 3) == Rational(-1, 14)
assert racah(2, 2, 2, 2, 2, 2) == Rational(-3, 70)
assert racah(7, 8, 7, 1, 7, 7, prec=4).is_Float
assert racah(5.5, 7.5, 9.5, 6.5, 8, 9) == -719 * sqrt(598) / 1158924
assert abs(racah(5.5, 7.5, 9.5, 6.5, 8, 9, prec=4) -
(-0.01517)) < S('1e-4')
def safe_racah(a, b, c, d, ee, ff):
""" Avoid the ValueError whenever the arguments don't fulfill the triangle
relation. """
try:
return float(racah(a, b, c, d, ee, ff, prec=None))
except ValueError or AttributeError:
return 0
def F(k, jf, l1, l2, ji):
verbose = False
# cg_coeff_homebrew = float(clebsch_gordan(l1, 1, l2, -1, k, 0)) # works, but takes arguments in different order compared to the sympy version
cg_coeff = float(wg.clebsch_gordan(l1, l2, k, 1, -1, 0))
if cg_coeff == 0:
return 0
w = float(wg.racah(ji, ji, l1, l2, k, jf))
# w = racah_w(ji, ji, l1, l2, k, jf) # returning strange values
if w == 0:
return 0
if verbose:
print(f'GC: {cg_coeff} W: {w}')
return pow(
(-1), (jf - ji - 1)) * (pow((2 * l1 + 1) * (2 * l2 + 1) * (2 * ji + 1),
(1.0 / 2.0))) * cg_coeff * w
def BM_Bracket00(n,l,N,L, l1,l2, lamda):
# Limit of the recurrence relation
const = ((fact[l1] + fact[l2] + fact[n+l] + fact[N+L]) -
(fact[2*l1] + fact[2*l2] + fact[n] + fact[N] +
fact[2*(n+l)+1] + fact[2*(N+L)+1]))
const += ((np.log(2*l+1)+np.log(2*L+1)) - ((l+L)*np.log(2)))
aux_sum = 0.
major = min((l+l1),(L+l2))
minor = max(abs(l-l1),abs(L-l2))
for x in range(minor, major+1):
try:
racah_aux = racah(l,L,l1,l2, lamda,x).evalf()
except AttributeError:
racah_aux = 0
aux_sum += ((2*x+1)*A_coeff(l1,l,l2,L, x)*racah_aux)
return np.exp(0.5*const) * aux_sum * ((-1)**(n+l+L-lamda))
def matrix_r2(n,l,N,L, n_q,l_q,N_q,L_q, lamda):
if((n_q<0) or (l_q<0) or (N_q<0) or(L_q<0)):
return 0
if(n_q == (n-1)):
# relations 1,3,4
if(l_q == l):
if(N_q == N):
if(L_q == L):
# rel 1
return 0.5*np.sqrt(n*(n+l+0.5))
else:
return 0
else:
return 0
elif(l_q == (l+1)):
if(N_q == (N-1)):
if(L_q == (L+1)):
# rel 3
try:
racah_aux = (racah(l,(l+1),L,(L+1),1,lamda)).evalf()
except AttributeError:
racah_aux = 0
return (((-1)**(lamda+L+l))*
np.sqrt(n*N*(l+1)*(L+1)) * racah_aux)
else:
return 0
elif(N_q == N):
if(L_q == (L-1)):
# rel 4
try:
racah_aux = (racah(l,(l+1),L,(L-1),1,lamda)).evalf()
except AttributeError:
racah_aux = 0
return (((-1)**(lamda+L+l))*
np.sqrt(n*L*(l+1)*(N+L+0.5)) * racah_aux)
else:
return 0
else:
return 0
else:
return 0
elif(n_q == n):
# relations 2,5,6
if(l_q == (l-1)):
if(N_q == (N-1)):
if(L_q == (L+1)):
# rel 5
try:
racah_aux = (racah(l,(l-1),L,(L+1),1,lamda)).evalf()
except AttributeError:
racah_aux = 0
return (((-1)**(lamda+L+l))*
np.sqrt(N*l*(n+l+0.5)*(L+1))*racah_aux)
else:
return 0
elif(N_q == N):
if(L_q == (L-1)):
# rel 6
try:
racah_aux = (racah(l,(l-1),L,(L-1),1,lamda)).evalf()
except AttributeError:
racah_aux = 0
return (((-1)**(lamda+L+l))*
np.sqrt(L*l*(n+l+0.5)*(N+L+0.5))*racah_aux)
else:
return 0
else:
return 0
elif(l_q == l):
if(N_q == (N-1)):
if(L_q == L):
# rel 2
return 0.5*np.sqrt(N*(N+L+0.5))
else:
return 0
else:
return 0
else:
return 0
else:
return 0
return ValueError
def test_racah():
assert racah(3,3,3,3,3,3) == Rational(-1,14)
assert racah(2,2,2,2,2,2) == Rational(-3,70)
assert racah(7,8,7,1,7,7, prec=4).is_Float
assert racah(5.5,7.5,9.5,6.5,8,9) == -719*sqrt(598)/1158924
assert abs(racah(5.5,7.5,9.5,6.5,8,9, prec=4) - (-0.01517)) < S('1e-4')